I think she may have babies already, judging by the way she digs. Blackbirds especially are very adept at digging at edges of concrete paths and newly planted plants, knowing that the soil is easily turned over and because of the moisture at those places, know that worms are often present there.
There is going to be a big problem when the young ones leave the nest as they are often unable to fly yet and spend a few days on the ground under hiding places.
A 12" wide scrap piece of tin/iron around the tree trunk 6' high will prevent the cats from climbing higher.
Cats will be on the lookout for the babies to leave though. Cats are not silly and they know.